Subalgebras of free algebras

Abstract

Abstract. We use non-commutative Jacobian matrix to get information on finitely generated subalgebras of a free Lie algebra. In particular, we show that the rank of such a subalgebra is equal to the left rank (i.e., to the maximal number of left independent rows) of the corresponding Jacobian matrix; this also yields an effective procedure for finding the rank of a finitely generated subalgebra.

Defining relations for automorphism groups of free algebras

“…Note that the statement of this corollary for infinite systems of elements is also true [9]. Free systems of elements in free algebras were studied in [12,20] via Fox derivatives.…”